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Write an absolute-value equation for each graph.

b.
a.
ty
2
-2 10
J
A
B
**

Write an absolute-value equation for each graph. b. a. ty 2 -2 10 J A B **-example-1

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To find the absolute-value equation for the given points (2,1), (3,2), (4,3), (2,1), (1,2), (0,3), (-1,4), (-2,5), observed symmetry around y = x + 1. The correct equation is y = |x - 2| + 1.

1. Initial Observation:

- Observe symmetry around the line y = x + 1, suggesting an absolute-value difference, |y - (x + 1)|.

2. Formulating an Initial Equation:

- Initially consider y = |y - (x + 1)|.

3. Refinement based on Observations:

- Notice that the distance should be from x = 2, not x = -1.

- Rewrite as y = |x + 1 - 2| + 1.

4. Verification with Given Points:

- Check if the equation y = |x - 2| + 1 fits the given points.

- For (2, 1): |1 - 2| + 1 = 2

- For (3, 2): |2 - 2| + 1 = 2

- ... and so on.

5. Final Confirmation:

- Confirm that the equation y = |x - 2| + 1 matches all given points, validating its correctness.

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